This paper introduces and motivates the use of Gaussian mixture models (GMM) for robust text-independent speaker identification. The individual Gaussian components of a GMM are shown to represent some general speaker-dependent spectral shapes that are effective for modeling speaker identify. The focus of this work is on applications which require high identification rates using short utterance from unconstrained conversational speech and robustness to degradations produced by transmission over a telephone channel. A complete experimental evaluation of the Gaussian mixture speaker model is conducted on a 49 speaker, conversational telephone speech database. The experiments examine algorithmic issues (initializations, variance limiting, model order selection), spectral variability robustness techniques, large population performance, and comparisons to other speaker modeling techniques (uni-modal Gaussian, VQ codebook, tied Gaussian mixture, and radial basis functions). The Gaussian mixture speaker model attains 96.8% identification accuracy using 5 second clean speech utterances and 80.8% accuracy using 15 second telephone speech utterances with a 49 speaker population and is shown to outperform the other speaker modeling techniques on an identical 16 speaker telephone speech task.